We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribed conditions)and are mechanically stable and temporally persistent.In terms of physics,air-water interf...We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribed conditions)and are mechanically stable and temporally persistent.In terms of physics,air-water interfaces are governed by the Young-Laplace equation.Mathematically they are surfaces of constant mean curvature which represent solutions of a nonlinear elliptic partial differential equation.Although explicit solutions of this equation can be obtained only in very special cases,it is -under moderately special circumstances-possible to establish the existence of a solution without actually solving the differential equation.We also derive criteria for mechanical stability and temporal persistence of an air layer.Furthermore we calculate the lifetime of a non-persistent air layer.Finally,we apply these tools to two examples which exhibit the symmetries of 2D lattices.These examples can be viewed as abstractions of the biological model represented by the aquatic fern Salvinia.展开更多
A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT mi...A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.展开更多
Precise control of a magnetically suspended double-gimbal control moment gyroscope （MSDGCMG） is of vital importance and challenge to the attitude positioning of spacecraft owing to its multivariable, nonlinear and s...Precise control of a magnetically suspended double-gimbal control moment gyroscope （MSDGCMG） is of vital importance and challenge to the attitude positioning of spacecraft owing to its multivariable, nonlinear and strong coupled properties. This paper proposes a novel linearization and decoupling method based on differential geometry theory and combines it with the internal model controller （IMC） to guarantee the system robustness to the external disturbance and parameter uncertainty. Furthermore, by introducing the dynamic compensation for the inner-gimbal rate-servo system and the magnetically suspended rotor （MSR） system only, we can eliminate the influence of the unmodeled dynamics to the decoupling control accuracy as well as save costs and inhibit noises effectively. The simulation results verify the nice decoupling and robustness performance of the system using the proposed method.展开更多
This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles)...This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles) on a triangular mesh consisting of congruent isosceles triangles. As an example, we perform global analysis of an Escher-style trick art, i.e., a simpler version of “Ascending and Descending”. After defining the local structure on the trick art, we analyze its global structure and attribute its paradox to a singular point (i.e., a singular triangle) at the center. Then, the endless “Penrose stairs” is described as a closed trajectory around the isolated singular point. The approach fits well with graphical projection and gives a simple and intuitive example of the interaction between global and local structures. We could deal with higher dimensional objects as well by considering n-simplices (n > 2) instead of triangles.展开更多
The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a ...The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge.To solve this problem,the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation(MJPVE)using Crab pulsar profile distortion is proposed in this paper.Firstly,through theoretical analysis,it is found that the pulsar profile distortion caused by the initial state error in some joint positionvelocity directions is very small.In other words,the accuracies of estimation in these directions are very low.Namely,the search dimension can be reduced,which in turn greatly reduces the computational load.Then,we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion.Finally,we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation.The experimental results show that compared with the grouping bi-chi-squared inversion method,MJPVE has high precision and extensive navigation information.展开更多
An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the...An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.展开更多
This research is concerned with coordinated standoff tracking, and a guidance law against a moving target is proposed by using differential geometry. We first present the geometry between the unmanned aircraft(UA) and...This research is concerned with coordinated standoff tracking, and a guidance law against a moving target is proposed by using differential geometry. We first present the geometry between the unmanned aircraft(UA) and the target to obtain the convergent solution of standoff tracking when the speed ratio of the UA to the target is larger than one. Then, the convergent solution is used to guide the UA onto the standoff tracking geometry. We propose an improved guidance law by adding a derivative term to the relevant algorithm. To keep the phase angle difference of multiple UAs, we add a second derivative term to the relevant control law. Simulations are done to demonstrate the feasibility and performance of the proposed approach. The proposed algorithm can achieve coordinated control of multiple UAs with its simplicity and stability in terms of the standoff distance and phase angle difference.展开更多
In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimensionn+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurfacex &...In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimensionn+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurfacex <sub class='a-plus-plus'>1</sub> x <sub class='a-plus-plus'>2</sub>...x <sub class='a-plus-plus'>n+1</sub>=const. We prove also that an affine complete, affine maximal surface is an elliptic paraboloid if its affine normals omit 4 or more directions in general position.展开更多
This paper presents the application of the proportional-integral-derivative （PID） controller to the flight control system （FCS） for two-dimensional （2D） differential geometric （DG） guidance and control problem...This paper presents the application of the proportional-integral-derivative （PID） controller to the flight control system （FCS） for two-dimensional （2D） differential geometric （DG） guidance and control problem. In particular, the performance of the designed FCS is investigated. To this end, the commanded angle-of-attack is firstly developed in the time domain using the classical DG formulations. Then, the classical PID controller is introduced to develop a FCS so as to form the 2D DG guidance and control system, and the PID controller parameters are determined by the Ziegler-Nichols method as well as the Routh-Hurwitz stability algorithm to guarantee the convergence of the system error. The results demonstrate that the designed controller yields a fast responding system, and the resulting DG guidance and control system is viable and effective in a realistic missile defense engagement.展开更多
By applying the framework of the tangent bundle geometry to the method of Lagrange multi- pliers,a geometric description of Chetaev's nonholonomic systems subjected to unilateral nonholonomic con- straints trod un...By applying the framework of the tangent bundle geometry to the method of Lagrange multi- pliers,a geometric description of Chetaev's nonholonomic systems subjected to unilateral nonholonomic con- straints trod unilateral holonomic constraints respectively in time-independent circumstances is presented.展开更多
Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom ...Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom induces a connection which is completely calculated. This allows us to discover the global and chiral properties of the space-time connection, with spin 2.展开更多
A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry.Moreover,a specialized whirlwind mil...A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry.Moreover,a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced.This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity.The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact,so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool.The practical results show that this new milling model is an effective method in machining complex three-dimensional surfaces.This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes.Some actual examples for manufacturing the freeform surfaces with this new model are given.展开更多
In view of differential geometry, the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometric...In view of differential geometry, the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometrical metrics is obtained. Moreover an example is used to illustrate our conclusions.展开更多
The description of modern differential geometry for time-dependent Chetaev nonholonomic mechanical systems with unilateral constraints is studied. By using the structure of exact contact manifold, the geometric framew...The description of modern differential geometry for time-dependent Chetaev nonholonomic mechanical systems with unilateral constraints is studied. By using the structure of exact contact manifold, the geometric framework of time- dependent nonholonomic mechanical systems subject to unilateral nonholonomic constraints and unilateral holonomic constraints respectively is presented.展开更多
This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.B...This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.展开更多
According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss c...According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss curvature, the proportion of the mid-surface area between before and after being developed is derived from the displacement variation of the mid-surface in the normal vector direction of the sheet metal during the sheet metal forming process. Hereby, based on the curve development theory in differential geometry, a novel diagonal point by point surface development method is put forward to estimate a complex cover panel＇s blank contour efficiently. By comparing the sample＇s development result of diagonal point by point surface development method with that of available one-step method, the validity of the proposed surface development method is verified.展开更多
The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux prof...The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.展开更多
Elliptical splats are used to represent and render the isosurface of volume data. The method consists of two steps. The first step is to extract points on the isosurface by looking up the case table. In the second ste...Elliptical splats are used to represent and render the isosurface of volume data. The method consists of two steps. The first step is to extract points on the isosurface by looking up the case table. In the second step, properties of splats are computed based on local geometry. Rendering is achieved using surface splatting algorithm. The obtained results show that the extraction time of isosurfaces can be reduced by a factor of three. So our approach is more appropriate for interactive visualization of large medical data than the classical marching cubes (MC) technique.展开更多
A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimens...A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate.展开更多
This paper proposes a novel category theoretic approach to describe protein’s shape, i.e., a description of their shape by a set of algebraic equations. The focus of the approach is on the relations between proteins,...This paper proposes a novel category theoretic approach to describe protein’s shape, i.e., a description of their shape by a set of algebraic equations. The focus of the approach is on the relations between proteins, rather than on the proteins themselves. Knowledge of category theory is not required as mathematical notions are defined concretely. In this paper, proteins are represented as closed trajectories (i.e., loops) of flows of triangles. The relations between proteins are defined using the fusion and fission of loops of triangles, where allostery occurs naturally. The shape of a protein is then described with quantities that are measurable with unity elements called “unit loops”. That is, protein’s shape is described with the loops that are obtained by the fusion of unit loops. Measurable loops are called “integral”. In the approach, the unit loops play a role similar to the role “1” plays in the set Z of integers. In particular, the author considers two categories of loops, the “integral” loops and the “rational” loops. Rational loops are then defined using algebraic equations with “integral loop” coefficients. Because of the approach, our theory has some similarities to quantum mechanics, where only observable quantities are admitted in physical theory. The author believes that this paper not only provides a new perspective on protein engineering, but also promotes further collaboration between biology and other disciplines.展开更多
基金funded by grants from the Deutsche Forschungsgemeinschaft,the Bundesministerium für Bildung und Forschung and the Landesgraduiertenfrderungsgesetz des Landes Baden-Württemberg
文摘We describe a few mathematical tools which allow to investigate whether air-water interfaces exist(under prescribed conditions)and are mechanically stable and temporally persistent.In terms of physics,air-water interfaces are governed by the Young-Laplace equation.Mathematically they are surfaces of constant mean curvature which represent solutions of a nonlinear elliptic partial differential equation.Although explicit solutions of this equation can be obtained only in very special cases,it is -under moderately special circumstances-possible to establish the existence of a solution without actually solving the differential equation.We also derive criteria for mechanical stability and temporal persistence of an air layer.Furthermore we calculate the lifetime of a non-persistent air layer.Finally,we apply these tools to two examples which exhibit the symmetries of 2D lattices.These examples can be viewed as abstractions of the biological model represented by the aquatic fern Salvinia.
基金supported by the National University of Defense Technology Innovation Support Project for Outstanding Graduate Student(B100303)
文摘A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.
文摘Precise control of a magnetically suspended double-gimbal control moment gyroscope （MSDGCMG） is of vital importance and challenge to the attitude positioning of spacecraft owing to its multivariable, nonlinear and strong coupled properties. This paper proposes a novel linearization and decoupling method based on differential geometry theory and combines it with the internal model controller （IMC） to guarantee the system robustness to the external disturbance and parameter uncertainty. Furthermore, by introducing the dynamic compensation for the inner-gimbal rate-servo system and the magnetically suspended rotor （MSR） system only, we can eliminate the influence of the unmodeled dynamics to the decoupling control accuracy as well as save costs and inhibit noises effectively. The simulation results verify the nice decoupling and robustness performance of the system using the proposed method.
文摘This paper shows the usefulness of discrete differential geometry in global analysis. Using the discrete differential geometry of triangles, we could consider the global structure of closed trajectories (of triangles) on a triangular mesh consisting of congruent isosceles triangles. As an example, we perform global analysis of an Escher-style trick art, i.e., a simpler version of “Ascending and Descending”. After defining the local structure on the trick art, we analyze its global structure and attribute its paradox to a singular point (i.e., a singular triangle) at the center. Then, the endless “Penrose stairs” is described as a closed trajectory around the isolated singular point. The approach fits well with graphical projection and gives a simple and intuitive example of the interaction between global and local structures. We could deal with higher dimensional objects as well by considering n-simplices (n > 2) instead of triangles.
基金supported in part by the National Natural Science Foundation of China(Nos.61873196,62373030,61772187)the Innovation Program for Quantum Science and Technology(No.2021ZD0303400)。
文摘The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge.To solve this problem,the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation(MJPVE)using Crab pulsar profile distortion is proposed in this paper.Firstly,through theoretical analysis,it is found that the pulsar profile distortion caused by the initial state error in some joint positionvelocity directions is very small.In other words,the accuracies of estimation in these directions are very low.Namely,the search dimension can be reduced,which in turn greatly reduces the computational load.Then,we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion.Finally,we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation.The experimental results show that compared with the grouping bi-chi-squared inversion method,MJPVE has high precision and extensive navigation information.
文摘An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.
基金Project supported by the National Natural Science Foundation of China(Nos.61273327 and 71201076)the Key Pre-research Fund of the PLA General Armament Department(No.9140A06050213BQX)the Natural Science Foundation of Jiangsu Province,China(No.BK2011564)
文摘This research is concerned with coordinated standoff tracking, and a guidance law against a moving target is proposed by using differential geometry. We first present the geometry between the unmanned aircraft(UA) and the target to obtain the convergent solution of standoff tracking when the speed ratio of the UA to the target is larger than one. Then, the convergent solution is used to guide the UA onto the standoff tracking geometry. We propose an improved guidance law by adding a derivative term to the relevant algorithm. To keep the phase angle difference of multiple UAs, we add a second derivative term to the relevant control law. Simulations are done to demonstrate the feasibility and performance of the proposed approach. The proposed algorithm can achieve coordinated control of multiple UAs with its simplicity and stability in terms of the standoff distance and phase angle difference.
基金The Project Supported by National Natural Science Foundation of China
文摘In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimensionn+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurfacex <sub class='a-plus-plus'>1</sub> x <sub class='a-plus-plus'>2</sub>...x <sub class='a-plus-plus'>n+1</sub>=const. We prove also that an affine complete, affine maximal surface is an elliptic paraboloid if its affine normals omit 4 or more directions in general position.
基金Throughout this paper, the word velocity will only be used to designate a vector quantitythe corresponding scalar will be denoted asspeed
文摘This paper presents the application of the proportional-integral-derivative （PID） controller to the flight control system （FCS） for two-dimensional （2D） differential geometric （DG） guidance and control problem. In particular, the performance of the designed FCS is investigated. To this end, the commanded angle-of-attack is firstly developed in the time domain using the classical DG formulations. Then, the classical PID controller is introduced to develop a FCS so as to form the 2D DG guidance and control system, and the PID controller parameters are determined by the Ziegler-Nichols method as well as the Routh-Hurwitz stability algorithm to guarantee the convergence of the system error. The results demonstrate that the designed controller yields a fast responding system, and the resulting DG guidance and control system is viable and effective in a realistic missile defense engagement.
基金the National Natural Science Foundation of China(No.19972010)the Qing Lan Project Foundation of Jiangsu Province of Chinathe Research Foundation of Suzhou Institute of Urban Construction & Environmental Protection of China
文摘By applying the framework of the tangent bundle geometry to the method of Lagrange multi- pliers,a geometric description of Chetaev's nonholonomic systems subjected to unilateral nonholonomic con- straints trod unilateral holonomic constraints respectively in time-independent circumstances is presented.
文摘Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom induces a connection which is completely calculated. This allows us to discover the global and chiral properties of the space-time connection, with spin 2.
基金China Postdoctoral Science Foundation(No.2005037348)Science and Technology Research Program of Hubei Province,Ministry of Education,China(No.D200612003)
文摘A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry.Moreover,a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced.This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity.The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact,so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool.The practical results show that this new milling model is an effective method in machining complex three-dimensional surfaces.This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes.Some actual examples for manufacturing the freeform surfaces with this new model are given.
基金supported by the National Natural Science Foundation of China (Grant No 10871218)
文摘In view of differential geometry, the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometrical metrics is obtained. Moreover an example is used to illustrate our conclusions.
基金Project supported by the National Natural Science Foundation of China （Grant No 10272021）, the Natural Science Foundation of High Education of Jiangsu Province, China （Grant No 04KJA130135） and the ＂Qing Lan＂ Project Foundation of Jiangsu Province, China.
文摘The description of modern differential geometry for time-dependent Chetaev nonholonomic mechanical systems with unilateral constraints is studied. By using the structure of exact contact manifold, the geometric framework of time- dependent nonholonomic mechanical systems subject to unilateral nonholonomic constraints and unilateral holonomic constraints respectively is presented.
文摘This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology.
文摘According to the characteristics of a complex cover panel, its geometry shape is described by the NURBS surface with great description capability. With the reference to the surface classification determined by Gauss curvature, the proportion of the mid-surface area between before and after being developed is derived from the displacement variation of the mid-surface in the normal vector direction of the sheet metal during the sheet metal forming process. Hereby, based on the curve development theory in differential geometry, a novel diagonal point by point surface development method is put forward to estimate a complex cover panel＇s blank contour efficiently. By comparing the sample＇s development result of diagonal point by point surface development method with that of available one-step method, the validity of the proposed surface development method is verified.
基金supported partially by the US NSF CAREER award program (ECCS-0645086)National Natural Science Foundation of China (No.F030119)+2 种基金Zhejiang Provincial Natural Science Foundation of China (Nos.Y1110354, Y6110751)the Fundamental Research Funds for the Central Universities of China (No.1A5000-172210101)the Natural Science Foundation of Ningbo (No.2010A610096)
文摘The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.
基金the Program of Advance Research between France and Chinese(No.PRA SI 03-03)the Region Rhone-Alpes of France within the Project"MIRA Research 2003"the Project of Image Guided Surgery of Shanghai,China(No.045115001)
文摘Elliptical splats are used to represent and render the isosurface of volume data. The method consists of two steps. The first step is to extract points on the isosurface by looking up the case table. In the second step, properties of splats are computed based on local geometry. Rendering is achieved using surface splatting algorithm. The obtained results show that the extraction time of isosurfaces can be reduced by a factor of three. So our approach is more appropriate for interactive visualization of large medical data than the classical marching cubes (MC) technique.
基金Supported by National Natural Science Foundation of China under Grant No. 11175063
文摘A technique of coordinate transformation is devised to overcome the computational difficulty associated with the direct transformation between eigenfunctions of three components of the geometric momentum on two-dimensional spherical surface, and the computations are firstly carried out in new coordinates and secondly the results are transformed back into the original coordinates. The eigenfunctions of different components of geometric momentum is explicitly demonstrated to transform under the spatial rotations in the precise way we anticipate.
文摘This paper proposes a novel category theoretic approach to describe protein’s shape, i.e., a description of their shape by a set of algebraic equations. The focus of the approach is on the relations between proteins, rather than on the proteins themselves. Knowledge of category theory is not required as mathematical notions are defined concretely. In this paper, proteins are represented as closed trajectories (i.e., loops) of flows of triangles. The relations between proteins are defined using the fusion and fission of loops of triangles, where allostery occurs naturally. The shape of a protein is then described with quantities that are measurable with unity elements called “unit loops”. That is, protein’s shape is described with the loops that are obtained by the fusion of unit loops. Measurable loops are called “integral”. In the approach, the unit loops play a role similar to the role “1” plays in the set Z of integers. In particular, the author considers two categories of loops, the “integral” loops and the “rational” loops. Rational loops are then defined using algebraic equations with “integral loop” coefficients. Because of the approach, our theory has some similarities to quantum mechanics, where only observable quantities are admitted in physical theory. The author believes that this paper not only provides a new perspective on protein engineering, but also promotes further collaboration between biology and other disciplines.
